# Find the coordinates of point A lying on the ordinate and equidistant from points B (1; -3) and C (2: 0).

Since point A lies on the ordinate, therefore the value of point A on the abscissa is 0, that is, the coordinate of point A (0, y).

Let’s use the formula for calculating the distance between two points A (xa, ya) and B (xb, yb) on the plane: AB = √ ((xb – xa) ^ 2 + (yb – ya) ^ 2).

Since point A is equidistant from points B and C, then AB = AC.

Substitute the coordinates of points A and B and C into the formula:

√ ((1 – 0) ^ 2 + (-3 – y) ^ 2) = √ ((2 – 0) ^ 2 + (0 – y) ^ 2).

√ (1 + 9 + 6 * y + y ^ 2) = √ (4 + y ^ 2).

10 + 6 * y + y ^ 2 = 4 + y ^ 2.

10 + 6 * y + y ^ 2 – 4 – y ^ 2 = 0.

6 * y = -6.

y = -1.

Therefore, the coordinates of point A (0; -1).

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